Geometry modeling and nonlinear reconstruction for x ray guided breast dot
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Geometry modeling and nonlinear reconstruction for X-ray guided breast DOT. Qianqian Fang + , David Boas + , Greg Boverman*, Quan Zhang + , Tina Kauffman + + Massachusetts General Hospital *Northeastern University. NTROI. Outline. Instrument overview Binary function based mesh generator

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Geometry modeling and nonlinear reconstruction for X-ray guided breast DOT

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Geometry modeling and nonlinear reconstruction for x ray guided breast dot

Geometry modeling and nonlinear reconstruction for X-ray guided breast DOT

Qianqian Fang+, David Boas+, Greg Boverman*, Quan Zhang+, Tina Kauffman+

+Massachusetts General Hospital

*Northeastern University

NTROI

SPIE Photonic West 2006


Outline

Outline

  • Instrument overview

  • Binary function based mesh generator

  • Iterative block solver

  • Reconstruction results

  • Summary

SPIE Photonic West 2006


Why combine x ray with dot

Why combine X-ray with DOT?

  • Mammography is low-cost and routinely used across the country

  • X-ray only provide morphological info.

  • DOT can provide functional measurement but is low-resolution.

    Combined X-ray/DOT imaging can help doctor’s assessment by overlaying functional image on top of structural image.

SPIE Photonic West 2006


System picture

System Picture

TOBI: tomographical optical breast

imaging system

Tomosynthesis: 3D Mammography

SPIE Photonic West 2006


Binary function based mesh generation

Binary function based mesh generation

Why another mesh generator?

  • Conventional method for mesh generation from medical images

    • segmentation and boundary extraction

    • surface smoothing

    • advance-front method

    • mesh optimization

  • What the new generator can offer?

    • anyone can understand and implement

    • no need for boundary extraction and smoothing

    • high quality elements, no need for mesh optimization

    • in some cases, may faster than conventional method

SPIE Photonic West 2006


Prologue distance function based mesh generation

Prologue: Distance function based mesh generation

  • Persson & Strang (MIT), 2004 SIAM Review: Simple mesh generation based on signed-distance functions

  • Pros:

    • simple

    • high quality

  • Cons:

    • difficult for compli-cated geometries

    • slow

http://www-math.mit.edu/~persson/mesh/

SPIE Photonic West 2006


Binary functions

Binary Functions

  • A binary function: inside or out side

1

-2

2

int binary_shape(double x, double y)

{

return (x>2. && x<-2. && y>2. && y<-2.

&& x*x+y*y>1.);

}

For medical images, only memory access is needed,

no arithmetic !

SPIE Photonic West 2006


Step 1 3 of 5

Step 1-3 of 5

  • Step 1: initial mesh

    • Truncating isotropic mesh by binary function

  • Step 2: boundary layer

    • Use Laplacian operator to find out the boundary layer

    • Reduce computationalcomplexity fromO(N) to O(N1/2) for2D, O(N) to O(N2/3)for 3D

  • Step 3: moving mesh

    • treat mesh as truss system, solve for physical equilibrium

SPIE Photonic West 2006


Step 4 of 5 boundary correction

Step 4 of 5: Boundary Correction

  • if nodes move outside the geometry

  • bi-sect search betweenPi and Pi+1

  • line search over a circle,find out the closest boundary point

Step 5 of 5: Re-Triangulation

  • Moving mesh will change mesh topology, without timely updating neighbor list, this may cause method to diverge.

  • Delaunay based triangulation (for example: QHull) can be used (only apply to the nodes within boundary layer)

SPIE Photonic West 2006


More complicated cases

More complicated cases

  • Mesh generation in 3D or in Rnspace

    • Step 1: using uniform grid as initial mesh

    • Step 4: the second line search in boundary correction is performed on a (hyper-)sphere surface

  • For medical images: segmentations

  • Anisotropic elements

  • Non-uniform mesh density

  • Quadtree or Octree

SPIE Photonic West 2006


Examples

Examples

SPIE Photonic West 2006


Iterative block solver for fem forward modeling

Iterative Block Solver for FEM forward modeling

  • Solving FEM forward equation: large scale, sparse, complex (or real) entries

  • Direct methods: SuperLU, UMFPACK, WSMP …

  • Iterative methods: CG, BiCG, GMRES, QMR …

  • QMR multi-RHS solver(Boyes&Seidl,1996): A[x1,x2,x3,..,xN]=[b1,b2,b3,…,bN] N: block size

SPIE Photonic West 2006


Solver performance

Solver Performance

  • mesh: 42122 nodes and 230745 elements

  • RF diffusion equation

optimal block size

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Results simulations

Results: Simulations

  • TOMO Slices Forward&Recon meshes

Slice#35

Slice#50

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Simulation cont d

Simulation – Cont’d

True absorption Recovered absorption w/o geometry modeling

A tumor

SPIE Photonic West 2006


Summary

Summary

  • Take home messages:

    • TOBI: RF+CW+MUX, can co-register with 2D or 3D mammography

    • Mesh generator is simple and easy to implement, good for mesh generation from medical images

    • Block solver is efficient in solving forward problems

  • Problems: mesh generator not entirely stable; some elements close to boundary are not perfect; 3D triangulation produces empty elements.

SPIE Photonic West 2006


Acknowledgements

Acknowledgements

  • Funding Agencies

    • NIH

    • NTROI

  • Avon Breast Cancer Center

    • Daniel Kopans

    • Richard Moore

    • Dianne Georgian-Smith

    • Jennifer Curry

    • Dianne Scourletis

    • Donna Burgess

    • Jayne Cormier

  • Lockheed Palo Alto Research Laboratories

    • William Boyse

  • Photon Migration Lab at MGH

    • Maria Franceschini

    • Stefan Carp

    • Juliette Selb

    • Elizabeth Hillman

    • Sol Diamond

    • Phill Jones

    • Danny Joseph

    • Ted Hupper

    • Anand Kumar

    • GW Krauss

    • George Themelis

    • ...

SPIE Photonic West 2006


Geometry modeling and nonlinear reconstruction for x ray guided breast dot

  • Questions?

SPIE Photonic West 2006


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